Question

Simplify: ${\left(0.00032\right)}^{3/5}\times {\left(\frac{8}{125}\right)}^{-4/3}$

Answer 1

${\left(0.00032\right)}^{3/5}={\left(0.2\right)}^{5\times \frac{3}{5}}={\left(0.2\right)}^3={\left(\frac{1}{5}\right)}^3=\frac{1}{125}$
Also ${\left(\frac{8}{125}\right)}^{-4/3}={\left(\frac{125}{8}\right)}^{4/3}={\left(\frac{5}{2}\right)}^{3\times \frac{4}{3}}={\left(\frac{5}{2}\right)}^4=\frac{625}{16}$
$\therefore$ Given expression $=\frac{1}{125}\times \frac{625}{6}=\frac{5}{16}$